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dxy orbital with metal orbitals which can directly overlap with
ligand orbitals. One possible mechanism could be spin–orbit
for the ligand superhyperfine coupling constants. It remains,
however, counterintuitive that a spin-polarization mechanism
should result in stronger coupling constants with increasing
bond length. To verify whether the calculated difference
between nitride and imide complexes was due to a difference
in the nitrogen coordination environment or bond length we
calculated the variation of the hyperfine coupling constants
À
coupling (SCO) admixture of the Cr N p* set of orbitals
{dxz,dyz} to the ground state. In a perturbation description this
admixture would be inversely proportional to the E-
({dxz,dyz})ÀE(dxy) energy separation which is dominated by
the p interaction with the axial ligand. Based on spectroscopic
data from the literature and the assumption that O2À and R
with Cr N distances for both the nitride and imide complex
À
À
N2À are comparable with respect to p-electron donation, the
energy difference E({dxz,dyz})ÀE(dxy) is expected to be
approximately twice as large in the nitride complexes as in
the imide analogues. This would accordingly justify the
inverse ratio between the 14N hyperfine couplings in the two
classes of systems.
keeping everything else constant. The Cr N bond lengths
À
were varied from 1.54 ꢀ, which is just below the experimental
distance in the nitride complexes, to 1.92 ꢀ, which approaches
À
the distance of a Cr N single bond. The results are depicted in
Figure 3.
It has recently been shown independently by Kaupp
et al.[17,18] and Neese[19] that DFT methods can yield insight
into mechanisms and magnitudes of metal and ligand hyper-
fine coupling constants in transition-metal complexes. We
have, along this venue, performed DFT calculations with the
Orca program[20] on a range of model systems to gain more
insight in the cause of the relative magnitude of the
experimentally determined hyperfine coupling constants. As
a model for the nitride complexes we use the experimentally
determined geometry of [Cr(N)(dbm)2], which is the parent
nitride complex of compounds 2–5. We replaced the phenyl
À
groups of the dbm ligand with hydrogens with a C H bond
length fixed at 0.96 ꢀ. As a model for the functionalized
complexes we used a linear methyl imide complex with an
equatorial coordination sphere which is identical to that of
our nitride model. Neese has tested different functionals and
basis sets.[19] We follow his choice of the B3LYP functional
combined with the VTZP basis supplemented with specially
flexible bases suitable for describing the core properties (CP
and IGLO-III, respectively) of Cr and N atoms. Details of the
calculations and a sample input file are available in the
Supporting Information.
Figure 3. Calculated variation of the isotropic hyperfine coupling
À
constants to nitrogen and chromium(V) as a function of the Cr N
bond length. The calculations employed the Orca program and the
B3LYP functional. The results are obtained with a VTZP basis set for
all atoms as well as with special basis sets adapted for description of
core properties of Cr and N atoms. In addition, two points for each of
the imide systems (at 1.62 ꢀ) illustrate the relative lack of sensitivity
The calculated values of the 14N and 53Cr hyperfine
coupling constants for our nitride model are À10.1 and
75.7 MHz, respectively, for the experimental geometry (d-
À
À
(Cr N) = 1.56 ꢀ). For the imide model (d(Cr N) = 1.62 ꢀ),
we obtained À47.3 and 44.4 MHz, respectively. The DFT
method thus reproduces the much larger 14N hyperfine
coupling constants in the imide complexes. It should be
noted that the quoted values are for calculations without
inclusion of second-order SCO. We found, in agreement with
our expectation and the findings of Neese, that inclusion of
SOC has only a marginal effect on the magnitude of the
chromium(V) hyperfine coupling and no effect on the
nitrogen hyperfine coupling. We also tested the importance
À À
towards bending of the Cr N C moiety (1708, 1608).
Surprisingly, the nitrogen hyperfine coupling constants
À
increase quite steeply with the Cr N distance for both classes
of compounds. Examination of the calculated spin and charge
densities reveals the cause of the paradox: as is the case for
many simple compounds, the dissociation of chromium
nitride (imide) complexes in the gas phase does not preserve
the oxidation states CrV and NÀIII but results instead in CrIII
and a triplet NÀI (Figure S7 and text in the Supporting
Information). As a limiting result of a calculation this is rather
unexceptional—the interesting fact is that this effect mani-
fests even at equilibrium bond distances and that the present
systems provide an exceptional case of an apparently simple
system where the notion of well-defined spectroscopic
oxidation states is experimentally challenged. Accordingly,
Wieghardt and co-workers found the internal oxidation state
À À
of lowering the symmetry by bending the Cr N C bonds in
the imide model and found no significant (< 5%) change in
the hyperfine coupling upon going from a linear geometry to a
bent geometry (1708 and 1608). We interpret the minimal
effect of spin–orbit coupling and of lowered symmetry as
signifying that the ligand field picture discussed above cannot
be used to rationalize the observed variation of the hyperfine
coupling constants. Instead we agree, based on the calculated
14N hyperfine coupling constants, with Kaupp et al. that spin
polarization in the strong Cr N bonds is the main mechanism
distribution within a chromium imido fragment {CrIV/III
-
À
ꢀ 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
Angew. Chem. Int. Ed. 2011, 50, 4480 –4483
Bendix, Jesper
